Gamow shell model study of the 17Ne(p, p) reaction and of isospin symmetry breaking in 18Na

TL;DR

The study addresses the unbound nucleus $^{18}$Na, a key intermediate in the sequential decay of $^{19}$Mg, by applying the coupled-channel Gamow shell model (GSM-CC) to unify structure and reaction calculations in an open quantum-system framework. The GSM uses the Berggren basis to include bound, resonant, and scattering states, while GSM-CC builds reaction channels from $^{17}$Ne states coupled to a proton and solves a generalized eigenvalue problem with non-orthogonal channels. The calculations reproduce the low-lying spectrum of $^{18}$Na, its decay widths, and the $^{17}$Ne$(p,p)$ cross section, revealing a narrow resonance at $E_r ≈ 1.553$ MeV with width ≈ 9 keV and a broader $0^-$/$1^-$/$3^-$ structure; the analysis shows a pronounced Thomas–Ehrman shift and isospin symmetry breaking in the mirror pair $^{18}$Na/$^{18}$N driven by the extended $s_{1/2}$ partial wave and continuum coupling. The work also quantifies mirror-energy differences relative to $^{18}$N, compares to the TES pattern seen in $^{16}$F/$^{16}$N, and demonstrates that GSM-CC can coherently describe both spectra and reaction observables for drip-line systems, with implications for interpreting experiments on exotic proton emitters.

Abstract

The unbound nucleus 18Na, acting as an intermediate nucleus in the sequential decay of 19Mg, is situated beyond the proton drip line. We employ the coupled-channel Gamow shell model (GSM-CC) to investigate the properties of 18Na, as well as the 17Ne(p, p) cross section. GSM-CC treats the nucleus as an open quantum system and provides a unified framework for studying both nuclear structure and reaction cross sections. Our calculations reproduce the energies and partial decay widths of low-lying states in 18Na, as well as the 17Ne(p, p) cross section. Additionally, the mirror nucleus 18N is also described. The isospin symmetry breaking induced by the Coulomb interaction and continuum coupling is clearly obtained in our description of 18Na and 18N properties, arising from the extended s1/2 partial wave. The isospin symmetry breaking in the 18Na/18N pair is compared to that occurring in the mirror pair 16F/16N, whereby similarities and differences are analyzed.

Figures (4)

• Figure 1: Low-lying energy spectrum of the $^{18}$Na calculated by GSM-CC, along the experimental data (Exp). Only states important for the description of cross sections are depicted. Excitation energies $E_r$ are provided in MeV relatively to the ground state of $^{17}$Ne. The calculated proton-emission width, in keV, is indicated by blue values next to the energy level. Experimental data are taken from Ref. ASSIE2012198.
• Figure 2: Excitation function of the $^{17}$Ne($p, p$) scattering reaction calculated with GSM-CC, along with the experimental data from Ref. ASSIE2012198 for comparison. The solid red line represents the GSM-CC results using a Hamiltonian that includes both nuclear and Coulomb interactions. The dotted blue line corresponds to the calculation considering only the Coulomb interaction. Energies and cross sections are defined in the center of mass frame at 180 degrees.
• Figure 3: Low-lying energy spectra of the $^{18}$Na and $^{18}$N nuclei obtained with GSM and GSM-CC (without and with corrections), along the experimental data (Exp). GSM-CC calculations without corrections are labeled by "f=1", while the "f" means the GSM-CC calculations with corrective factors. The energy spectra obtained from GSM and GSM-CC (f=1) calculations are referenced with respect to the 2$^-$ state energy calculated from GSM-CC (f). The 2$^-$ state energies of GSM-CC (f) and their experimental values are put to zero to be able to compare their mirror energy difference (MED). Excitation energies $E_x$ are given in MeV. Experimental data of $^{18}$N are taken from Ref. PhysRevC.104.L041301.
• Figure 4: GSM density distributions of valence protons (neutrons) of the $^{17}$Ne ($^{17}$N) ground states, respectively. The used cores for both calculations are indicated in brackets.